Laser welding is an attractive process for producing stiff, strong, lightweight structures. FIG. 1 is a drawing of a corrugated core sandwich panel produced by laser welding with a high strength and stiffness to weight ratio. The illustrated panel is referred to as a LASCOR panel, and is representative of the prior art. As shown in FIG. 1, the LASCOR panel consists of a pair of face sheets welded to a corrugated core. The face sheets are attached to the core using autogeneous laser stake welds, which means that no filler material is used. As shown, the corrugated core has upper and lower generally flat portions and the face sheets are welded to the flat portions. As such, the autogeneous welds act to join two generally parallel thin pieces of metal to one another. As will be clear to those of skill in the art, the panel shown in FIG. 1 has a higher stiffness in a direction parallel to the corrugations than in a direction perpendicular to the corrugations.